Supposing someone has a cold sore and has o.Ral sex with someone, can they cause the person to get a cold sore down below?

Herpes. 75% of americans have herpes type one. Most got this as children from family members. Once one has been infected with one of the herpes viruses they cannot be reinfected at any other part of their body with the same virus. It is always best to know your herpes status. In your scenario the answer is yes, of course they can get herpes anywhere in the body if they have never been exposed before.